I'm in the USA, so I can only give my opinion from that point of view.
Police can come to your house and knock on your door whenever they want, but they need a reason to go to your house in the first place. Unless you have done something ridiculous, like tell your doctor about an exit plan,, etc, they likely aren't going to stop by.
I don't think that using a VPN or Tor would make a difference: your police force doesn't have the manpower to monitor internet traffic like that. And besides, if you are using https sites, then the police would have to break end-to-end encryption on top of that. And, frankly, we are too small of potatoes for the NSA. If the federal government did crack this type of encryption, they sure would not want to spill the beans on a bunch of suicidal people.. LOL.
No, the weak point would be delivery. I think your seller is far more likely to tell authorities than some computer network sniffing software.
Ive heard people using false names and gift credit cards for purchasing stuff on the dark web, if for no other reason than to deny ownership if someone shows up. I've never done that myself.
HTH